%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP020^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:25 AM UTC 2026
% Result : Theorem 7.59s 2.78s
% Output : Refutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 66
% Syntax : Number of formulae : 146 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 698 ( 117 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1801 ( 80 ~; 75 |; 82 &;1362 @)
% ( 0 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 10 con; 0-2 aty)
% Number of variables : 276 ( 0 ^; 243 !; 33 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(tp__ty_2Enum_2Enum_type,type,
tp__ty_2Enum_2Enum: $tType ).
thf(tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum_type,type,
tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $tType ).
thf(bool_decl,type,
bool: del ).
thf(arr_decl,type,
arr: del > del > del ).
thf(mem_decl,type,
mem: $i > del > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(lam_decl,type,
lam: del > ( $i > $i ) > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(inj__o_decl,type,
inj__o: $o > $i ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $i ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $i ).
thf(c_2Emin_2E_3D_3D_3E_decl,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Ebool_2E_5C_2F_decl,type,
c_2Ebool_2E_5C_2F: $i ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $i ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D: del > $i ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21: del > $i ).
thf(c_2Epred__set_2EUNIV_decl,type,
c_2Epred__set_2EUNIV: del > $i ).
thf(ty_2Epair_2Eprod_decl,type,
ty_2Epair_2Eprod: del > del > del ).
thf(c_2Epred__set_2ECROSS_decl,type,
c_2Epred__set_2ECROSS: del > del > $i ).
thf(c_2Epred__set_2EBIJ_decl,type,
c_2Epred__set_2EBIJ: del > del > $i ).
thf(ty_2Enum_2Enum_decl,type,
ty_2Enum_2Enum: del ).
thf(inj__ty_2Enum_2Enum_decl,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(surj__ty_2Enum_2Enum_decl,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
thf(inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum_decl,type,
inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i ).
thf(surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum_decl,type,
surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ).
thf(c_2Ebool_2E_3F_decl,type,
c_2Ebool_2E_3F: del > $i ).
thf(50,axiom,
? [A: $i] :
( ( mem @ A @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ A ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).
thf(185,plain,
? [A: $i] :
( ( mem @ A @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ A ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(3,axiom,
! [A: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum) ).
thf(70,plain,
! [A: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2ENOT__NOT) ).
thf(169,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) ) )
| ( p @ C ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( ( p @ ( ap @ B @ D ) )
| ( p @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM) ).
thf(181,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) ) )
| ( p @ C ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( ( p @ ( ap @ B @ D ) )
| ( p @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
! [A: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ A ) @ ty_2Enum_2Enum ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Enum_2Enum) ).
thf(199,plain,
! [A: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ A ) @ ty_2Enum_2Enum ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
= ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
= $true )
= ( p @ A ) )
& ( ( $false
= ( p @ A ) )
= ( ~ ( p @ A ) ) )
& ( ( ( p @ A )
= $false )
= ( ~ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEQ__CLAUSES) ).
thf(114,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
=> ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ~ ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__imp) ).
thf(82,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
=> ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ~ ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(146,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
? [A: $i] :
( ( mem @ A @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ A ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( mem @ A @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ A ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(68,plain,
~ ? [A: $i] :
( ( mem @ A @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ A ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(69,plain,
! [A: $i] :
( ~ ( mem @ A @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ A ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(31,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(138,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(67,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
& ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__conj) ).
thf(234,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
& ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(9,axiom,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
=> ( A
= ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) ).
thf(88,plain,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
=> ( A
= ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ C @ D ) )
| ( p @ B ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) )
| ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ELEFT__FORALL__OR__THM) ).
thf(170,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ C @ D ) )
| ( p @ B ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(22,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ( p @ B )
& ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ B )
& ( p @ ( ap @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM) ).
thf(115,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ( p @ B )
& ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ B )
& ( p @ ( ap @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
( ! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) )
& ( ( ~ $true ) = $false )
& ( ( ~ $false ) = $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ENOT__CLAUSES) ).
thf(184,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(18,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ A )
=> ( ~ ( p @ A )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2EAND__INV__IMP) ).
thf(110,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(125,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39,axiom,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(157,plain,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(51,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(189,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(37,axiom,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(152,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(65,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(228,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(41,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(164,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(47,axiom,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) ).
thf(179,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(24,axiom,
! [A: del,B: del] : ( mem @ ( c_2Epred__set_2ECROSS @ A @ B ) @ ( arr @ ( arr @ A @ bool ) @ ( arr @ ( arr @ B @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A @ B ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECROSS) ).
thf(121,plain,
! [A: del,B: del] : ( mem @ ( c_2Epred__set_2ECROSS @ A @ B ) @ ( arr @ ( arr @ A @ bool ) @ ( arr @ ( arr @ B @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A @ B ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(35,axiom,
! [A: del,B: del] : ( mem @ ( c_2Epred__set_2EBIJ @ A @ B ) @ ( arr @ ( arr @ A @ B ) @ ( arr @ ( arr @ A @ bool ) @ ( arr @ ( arr @ B @ bool ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EBIJ) ).
thf(147,plain,
! [A: del,B: del] : ( mem @ ( c_2Epred__set_2EBIJ @ A @ B ) @ ( arr @ ( arr @ A @ B ) @ ( arr @ ( arr @ A @ bool ) @ ( arr @ ( arr @ B @ bool ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(29,axiom,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(132,plain,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
thf(206,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(220,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(8,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ( p @ B )
| ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EDISJ__SYM) ).
thf(85,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ( p @ B )
| ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
thf(201,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_3F) ).
thf(97,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(224,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(64,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( B = C )
= ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEQ__SYM__EQ) ).
thf(225,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( B = C )
= ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(6,axiom,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(77,plain,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(58,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(212,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
| ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__disj) ).
thf(173,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
| ( p @ C ) ) )
= ( ( ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ B )
| ( p @ C )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(28,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ B @ bool ) )
=> ( ( ? [E: $i] :
( ( mem @ E @ ( arr @ A @ B ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A @ B ) @ E ) @ C ) @ D ) ) ) )
= ( ? [E: $i] :
( ( mem @ E @ ( arr @ B @ A ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ B @ A ) @ E ) @ D ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EBIJ__SYM) ).
thf(129,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ B @ bool ) )
=> ( ( ? [E: $i] :
( ( mem @ E @ ( arr @ A @ B ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A @ B ) @ E ) @ C ) @ D ) ) ) )
= ( ? [E: $i] :
( ( mem @ E @ ( arr @ B @ A ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ B @ A ) @ E ) @ D ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) ).
thf(73,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(55,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
=> ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
=> $true )
= $true )
& ( ( $false
=> ( p @ A ) )
= $true )
& ( ( ( p @ A )
=> ( p @ A ) )
= $true )
& ( ( ( p @ A )
=> $false )
= ( ~ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__CLAUSES) ).
thf(205,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(42,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( ~ ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ~ ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ENOT__EXISTS__THM) ).
thf(166,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( ~ ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ~ ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(40,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ B )
& ( p @ ( ap @ C @ D ) ) ) )
= ( ( p @ B )
& ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM) ).
thf(161,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ B )
& ( p @ ( ap @ C @ D ) ) ) )
= ( ( p @ B )
& ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(36,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) )
& ( p @ C ) ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) ) )
& ( p @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM) ).
thf(149,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) )
& ( p @ C ) ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ B @ D ) ) )
& ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( ( p @ A )
| ( p @ B ) )
=> $false )
= ( ( ( p @ A )
=> $false )
=> ( ~ ( p @ B )
=> $false ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2EOR__DUAL2) ).
thf(176,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
| ( p @ B ) )
= ( ~ ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(23,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_or_p) ).
thf(118,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(54,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ~ ( p @ A )
=> ( ( p @ A )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EF__IMP) ).
thf(204,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(20,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(113,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ( p @ A )
=> $false )
=> ( ( ( p @ A )
=> $false )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2EAND__INV2) ).
thf(219,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(80,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(instance,[status(thm)],[77]) ).
thf(81,plain,
~ ( p @ ( inj__o @ $false ) ),
inference(simp,[status(thm)],[80]) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(76,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( p @ A )
=> $false )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__F) ).
thf(103,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ B )
| ( p @ ( ap @ C @ D ) ) ) ) )
= ( ( p @ B )
| ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM) ).
thf(140,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ B )
| ( p @ ( ap @ C @ D ) ) ) ) )
= ( ( p @ B )
| ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ B @ D ) ) )
& ( p @ C ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ B @ D ) )
& ( p @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ELEFT__AND__FORALL__THM) ).
thf(91,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ( p @ ( ap @ B @ D ) ) )
& ( p @ C ) )
= ( ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ B @ D ) )
& ( p @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(62,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_5C_2F) ).
thf(223,plain,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(30,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
= ( ~ ( p @ B ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__neg) ).
thf(135,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
= ( ~ ( p @ B ) ) )
= ( ( ( p @ A )
| ( p @ B ) )
& ( ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(57,axiom,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(209,plain,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
thf(111,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(112,plain,
~ ( p @ c_2Ebool_2EF ),
inference(polarity_switch,[status(thm)],[111]) ).
thf(25,axiom,
! [A: del] : ( mem @ ( c_2Epred__set_2EUNIV @ A ) @ ( arr @ A @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EUNIV) ).
thf(123,plain,
! [A: del] : ( mem @ ( c_2Epred__set_2EUNIV @ A ) @ ( arr @ A @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(38,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ( p @ B )
| ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ C @ D ) ) ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( ( p @ B )
| ( p @ ( ap @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM) ).
thf(154,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ ( arr @ A @ bool ) )
=> ( ( ( p @ B )
| ? [D: $i] :
( ( mem @ D @ A )
& ( p @ ( ap @ C @ D ) ) ) )
= ( ? [D: $i] :
( ( mem @ D @ A )
& ( ( p @ B )
| ( p @ ( ap @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(33,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
thf(143,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_ex_p) ).
thf(231,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(13,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(99,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(59,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(218,plain,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ ( arr @ B @ bool ) ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ? [E: $i] :
( ( mem @ E @ B )
& ( p @ ( ap @ ( ap @ C @ D ) @ E ) ) ) ) )
= ( ? [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
& ! [E: $i] :
( ( mem @ E @ A )
=> ( p @ ( ap @ ( ap @ C @ E ) @ ( ap @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ESKOLEM__THM) ).
thf(104,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ ( arr @ B @ bool ) ) )
=> ( ( ! [D: $i] :
( ( mem @ D @ A )
=> ? [E: $i] :
( ( mem @ E @ B )
& ( p @ ( ap @ ( ap @ C @ D ) @ E ) ) ) ) )
= ( ? [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
& ! [E: $i] :
( ( mem @ E @ A )
=> ( p @ ( ap @ ( ap @ C @ E ) @ ( ap @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i] :
( ( mem @ A @ ty_2Enum_2Enum )
=> ( A
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Enum_2Enum) ).
thf(107,plain,
! [A: $i] :
( ( mem @ A @ ty_2Enum_2Enum )
=> ( A
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( ~ ( p @ A )
| ( p @ B ) )
=> $false )
= ( ( p @ A )
=> ( ~ ( p @ B )
=> $false ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2EOR__DUAL3) ).
thf(126,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ~ ( p @ A )
| ( p @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(78,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(instance,[status(thm)],[77]) ).
thf(79,plain,
p @ ( inj__o @ $true ),
inference(simp,[status(thm)],[78]) ).
thf(11,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
= ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Esat_2Edc__eq) ).
thf(94,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ! [C: $i] :
( ( mem @ C @ bool )
=> ( ( ( p @ A )
= ( ( p @ B )
= ( p @ C ) ) )
= ( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(237,plain,
( ~ $true
| ( ( p @ c_2Ebool_2EF )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[224,112]) ).
thf(238,plain,
( ( p @ c_2Ebool_2EF )
!= ( p @ c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[237]) ).
thf(239,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(simp,[status(thm)],[238]) ).
thf(240,plain,
( ~ $true
| ( ( p @ ( inj__o @ $true ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[79,112]) ).
thf(241,plain,
( ( p @ ( inj__o @ $true ) )
!= ( p @ c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[240]) ).
thf(242,plain,
( ( inj__o @ $true )
!= c_2Ebool_2EF ),
inference(simp,[status(thm)],[241]) ).
thf(14,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(100,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(292,plain,
$false,
inference(e,[status(thm)],[185,70,169,181,199,114,82,146,68,69,138,234,88,170,115,184,110,125,157,189,152,228,164,179,121,147,132,206,220,85,201,97,224,225,77,212,173,129,73,205,166,161,149,176,118,204,113,219,81,76,103,140,91,223,135,209,112,123,154,143,231,99,218,104,107,126,79,94,239,242,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP020^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n009.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 19:33:30 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.64/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.07/0.69 % [INFO] Parsing done (176ms).
% 1.40/0.70 % [INFO] Running in sequential loop mode.
% 1.99/0.91 % [INFO] eprover registered as external prover.
% 1.99/0.92 % [INFO] Scanning for conjecture ...
% 1.99/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 65 axioms. Running axiom selection ...
% 2.21/1.13 % [INFO] Axiom selection finished. Selected 65 axioms (removed 0 axioms).
% 2.63/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 2.63/1.29 % [INFO] Type checking passed.
% 2.63/1.29 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.59/2.78 % External prover 'e' found a proof!
% 7.59/2.78 % [INFO] Killing All external provers ...
% 7.59/2.78 % Time passed: 2480ms (effective reasoning time: 2076ms)
% 7.59/2.78 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.59/2.78 % Axioms used in derivation (65): stp_inj_mem_ty_2Enum_2Enum, ax_true_p, mem_c_2Ebool_2E_7E, conj_thm_2Ebool_2ETRUTH, conj_thm_2Ebool_2ELEFT__FORALL__OR__THM, lam_tp, mem_c_2Ebool_2ET, mem_c_2Ebool_2E_3F, ax_neg_p, mem_c_2Ebool_2E_2F_5C, stp_inj_surj_o, conj_thm_2Esat_2EAND__INV2, conj_thm_2Ebool_2EIMP__CLAUSES, conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM, conj_thm_2Ebool_2EEQ__CLAUSES, conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM, stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum, conj_thm_2Eutil__prob_2ENUM__2D__BIJ, ax_imp_p, ax_eq_p, stp_iso_mem_ty_2Enum_2Enum, conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM, mem_c_2Epred__set_2EUNIV, conj_thm_2Ebool_2EDISJ__SYM, funcext, mem_c_2Ebool_2E_21, conj_thm_2Esat_2Edc__conj, conj_thm_2Esat_2ENOT__NOT, conj_thm_2Ebool_2EEQ__SYM__EQ, stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum, conj_thm_2Esat_2EOR__DUAL3, stp_inj_surj_ty_2Enum_2Enum, conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM, ax_and_p, conj_thm_2Ebool_2ENOT__CLAUSES, conj_thm_2Esat_2Edc__imp, mem_c_2Emin_2E_3D, conj_thm_2Esat_2EAND__INV__IMP, conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM, mem_c_2Ebool_2EF, conj_thm_2Esat_2Edc__eq, ax_or_p, ax_all_p, mem_c_2Epred__set_2ECROSS, conj_thm_2Ebool_2EF__IMP, conj_thm_2Epred__set_2EBIJ__SYM, conj_thm_2Esat_2EOR__DUAL2, ax_ex_p, mem_c_2Epred__set_2EBIJ, ap_tp, stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum, conj_thm_2Esat_2Edc__neg, beta, conj_thm_2Ebool_2ESKOLEM__THM, mem_c_2Ebool_2E_5C_2F, ax_false_p, conj_thm_2Esat_2Edc__disj, stp_iso_mem_o, mem_c_2Emin_2E_3D_3D_3E, conj_thm_2Ebool_2EIMP__F, conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM, conj_thm_2Ebool_2ELEFT__AND__FORALL__THM, conj_thm_2Ebool_2ENOT__EXISTS__THM, stp_inj_mem_o, conj_thm_2Ebool_2EIMP__ANTISYM__AX
% 7.59/2.78 % No. of inferences in proof: 146
% 7.59/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2480 ms resp. 2076 ms w/o parsing
% 8.19/2.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.61/2.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------